Signals may be used to transmit data over distances. In optical communication systems, for example, data may be modulated on one or more optical wavelengths to produce modulated optical signals that may be transmitted over optical waveguides such as optical fibers. One modulation scheme that may be used in optical communication systems is phase shift keying in which data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength represents symbols encoding one or more bits. In a binary phase-shift keying (BPSK) modulation scheme, for example, two phases may be used to represent 1 bit per symbol. In a quadrature phase-shift keying (QPSK) modulation scheme, four phases may be used to encode 2 bits per symbol. Other phase shift keying formats include differential phase shift keying (DPSK) formats and variations of phase shift keying and differential phase shift keying formats, such as return-to-zero DPSK (RZ-DPSK).
To receive the data, the signals may be detected and demodulated. In phase modulated optical communication systems, for example, coherent optical receivers may use coherent detection to detect modulated optical signals and may provide sensitivity advantages over receivers using non-coherent detection. Digital signal processing (DSP) may be implemented in such systems for processing the received signals to provide demodulated data. Digital signal processing of the received signals provides speed and flexibility and may be used to perform a variety of functions including estimation of the carrier phase of the received signals and data detection using the estimated carrier phase.
Coherent detection involves use of a local oscillator signal that is mixed with the received signal. Unfortunately, due to a variety of factors, the local oscillator output may change in the range of MHz to GHz in optical detection systems and may drift with time. To achieve highly accurate demodulation of the optical signal, it is desirable to compensate for any frequency offset between the received signal and the frequency of the local oscillator signal. Reliable frequency offset compensation methods should be capable of covering a wide range of frequency offsets and be adaptive to possible frequency drift.